CN101887239A - Adaptive industrial process optimal control system and method - Google Patents

Abstract

The invention relates to an adaptive industrial process optimal control system, which comprises an intelligent detecting instrument, a DCS system and a host computer, wherein the intelligent detecting instrument is connected with an industrial process object; the industrial process object, the intelligent detecting instrument, the DCS system and the host computer are connected with one another in turn; and the host computer comprises an information acquisition module, an initialization module, a constraint conversion module, an adaptive solution module, an iterative optimization module, a convergence judgment module and a result output module. The invention also provides an adaptive industrial process optimal control method. The system and the method can accurately and stably find the optimal solution for a non-linear industrial process optimal control problem, have high optimization solution efficiency, and are the optimal control system and method having extensive applicability.

Description

Self-adaptive industrial process optimal control system and method

Technical Field

The invention relates to the field of industrial process optimal control, in particular to a self-adaptive industrial process optimal control system.

Background

Any industrial process is, strictly speaking, a dynamic process, i.e. the state variables (such as flow, temperature, pressure, liquid level, etc.) describing the process change with the evolution of time and the spatial shift. The dynamic process is described by differential equations or difference equations and is called a dynamic model. The optimal control is to control the operation variables in the dynamic model, so that the performance index of the process is optimal.

Although some existing optimal control problem solving methods can find solutions of the optimal control problems in the industrial process, the problems of slow convergence and instability often occur, the solutions can also fall into local optimization, the global optimality of the obtained solutions is difficult to guarantee, and the solutions of the optimal control problems are stable and fast.

Disclosure of Invention

In order to overcome the defects that the existing industrial process optimal control system and method are difficult to find the optimal solution accurately and quickly and have poor applicability, the invention provides the adaptive industrial process optimal control system and method which can find the global optimal solution accurately, have high solving efficiency and wide applicability.

The technical scheme adopted by the invention for solving the technical problems is as follows:

the utility model provides an industrial process optimal control system of self-adaptation, includes on-spot intelligent instrument, DCS system and the host computer of being connected with industrial process object, intelligent detection instrument, DCS system and host computer link to each other in proper order, the host computer include:

the initialization module is used for setting initial parameters, optimizing discretization and initial assignment of variables z (t), and comprises the following specific steps:

(3.1) time domain [ t₀，t_f]The average division into n small segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]，

Wherein t is_n＝t_f(ii) a The length of each time segment is h ═ t (t)_f-t₀) N, where t₀Denotes the starting time, t_fIndicating a termination time;

(3.2) discretizing the optimized variable z (t) on the time segment (3.1), replacing z (t) with a variable z consisting of n segment constants, and selecting an arbitrary constant as an initial value z of a decision variable⁰；

(3.3) setting a convergence precision value zeta for judging whether the iterative optimization is terminated, and stopping the iteration when the iterative error of the optimization target value is smaller than zeta; taking an initial value of the iteration times k as 0;

(3.4) setting an initial step size alpha 0 of iterative search;

the constraint conversion module is used for processing the control variable boundary constraint in the optimization process through the intermediate variable and adopting the following conversion equation:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

will have boundary constraint u_min≤u(t)u_maxIs replaced by a trigonometric function expression of an intermediate variable z (t) which is not bound by a boundary, where the indices min, max represent the minimum and maximum values, respectively, u (t)_min、u_maxRespectively corresponding to the lower bound and the upper bound of the control variable, and solving by taking z (t) as an optimization variable;

the self-adaptive solving module is used for solving a normal differential equation set of an optimal control problem of the industrial process, providing state variable and covariate variable information for gradient calculation of the iterative optimization module, and providing target function information for convergence condition judgment of the convergence judgment module, and is completed by adopting the following steps:

(4.1) solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0(i＝1，2，...，m) (2)

wherein f represents a differential function variable, x (t) is a variable consisting of m state variables, x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀A value of (d);

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><mi>d</mi><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>t</mi><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math>

i＝1，2，...，m

(3)

wherein,ψ is a given objective functionNon-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) Is a covariant lambda_iAt terminal time t_fA value of (d);

(4.3) calculating an objective function value from the obtained state variables and decision variables:

an iterative optimization module for searching a decision variable z for optimizing an objective function J^＊The method is completed by adopting the following steps, the superscripts k all represent the iteration times, and the initial assignment is zero:

(5.1) calling an adaptive solving module, and saving the obtained state variable, the obtained co-state variable and the obtained objective function value, wherein the objective function value is the current target value J^k；

(5.2) calculating the current gradient g^kThe superscript T represents the transpose of the variable or matrix, i.e. the search direction of the iterative optimization:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msub><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if k is 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, the step factor l is determined by iterating the information of the current point and the previous point^k：

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

Wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mo>=</mo><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Passes to an adaptive solution module to calculate a new objective function value J^k+1Then entering a convergence judgment module;

a convergence judgment module: the method is used for judging whether the target result obtained by the iteration optimizing module meets the convergence condition:

|J^k-J^k+1|≤ζ (11)

wherein, J^kAnd J^k+1Respectively representing objective function values obtained by the k-th iterative computation and the (k +1) -th iterative computation, stopping the iterative optimization computation if the above expression (11) is satisfied, and the absolute value of the error between the target value obtained by the current iteration and the target value obtained by the previous iteration is not more than the set convergence precision zeta, and z is^k+1Is the optimal decision variable z^*(＝z^k+1)，J^k+1Is the optimum target value J^*(＝J^k+1) Will z^*、J^*And the corresponding iteration times (k +1) are saved in a result output module; if the above equation (11) is not satisfied, the target value J is stored^k+1And taking k as k +1, and then returning to the iterative optimization module to perform a new round of iterative solution.

As a preferred solution: the upper computer also comprises an information acquisition module which is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument.

Further, the upper computer also comprises a result output module which is used for outputting the optimal decision trajectory z obtained by the iteration optimizing module^*(t) conversion into an optimal control trajectory u by equation (1)^*(t), optimal decision trajectory z^*(t) is represented by the variable z^＊Expressed in time intervals, then u is^*And (t) transmitting to the DCS, and displaying the obtained optimization result information in the DCS.

An adaptive optimal control method for an industrial process, comprising the following steps:

1) specifying state variables and control variables in a DCS system, and setting upper and lower boundaries u of the control variables according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd the sampling period of the DCS, and the historical data of corresponding variables in the DCS database, the upper and lower boundary values u of the control variables_max、u_minTransmitting to an upper computer;

2) and (3) processing the control variable boundary constraint in the optimization process through the intermediate variable, and adopting the following conversion equation:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

will have boundary constraint u_min≤u(t)≤u_maxIs replaced by an intermediate variable that is not bound by a boundaryz (t), where the indices min, max represent the minimum and maximum values, respectively, u_min、u_maxRespectively corresponding to the lower bound and the upper bound of the control variable, and solving by taking z (t) as an optimization variable;

3) setting initial parameters of the module, initializing data input by a DCS, and completing the steps as follows:

(3.1) time domain [ t₀，t_f]The average division into n small segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]Wherein t is_n＝t_f(ii) a The length of each time segment is h ═ t (t)_f-t₀) N, where t₀Denotes the starting time, t_fIndicating a termination time;

(3.2) discretizing the optimized variable z (t) on the time segment (3.1), replacing z (t) with a variable z consisting of n segment constants, and selecting an arbitrary constant as an initial value z of a decision variable⁰；

(3.3) setting a convergence precision value zeta for judging whether the iterative optimization is terminated, and stopping the iteration when the iterative error of the optimization target value is smaller than zeta; taking an initial value of the iteration times k as 0;

(3.4) setting the initial step size alpha 0 of the iterative search to be more than 0;

4) the optimization variable z of the current iteration step is equal to z^kSubstituting into the self-adaptive solving module, and when the iteration number k is 0, z is equal to z⁰Calculating the current state variable and the covariate and obtaining the corresponding current target value J^kThe method comprises the following implementation steps:

(4.1) solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0(i＝1，2，...，m) (2)

wherein f represents a differential function variable, x (t) is a variable consisting of m state variables, x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀A value of (d);

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><mi>d</mi><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>t</mi><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math>

i＝1，2，...，m

(3)

wherein,

ψ is a given objective functionNon-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) Is a covariant lambda_iAt terminal time t_fA value of (d);

(4.3) calculating an objective function value from the obtained state variables and decision variables:

5) calculating the search direction and step length of iterative optimization by the state variable and the covariate information obtained by the self-adaptive solving module, solving the decision variable z which enables the objective function J to be closer to the optimal value, and implementing the iterative optimization, wherein the superscript k represents the iteration times, and the initial assignment is zero:

(5.1) calling the calculation result in the step 4), and saving the obtained state variable, the obtained co-state variable and the obtained objective function value, wherein the objective function value is the current target value J^k；

(5.2) calculating the current gradient g^kThe superscript T represents the transpose of the variable or matrix, i.e. the search direction of the iterative optimization:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msub><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if k is 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, the step factor l is determined by iterating the information of the current point and the previous point^k：

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

Wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mo>=</mo><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Passes to step (5.4) to calculate a new value of the objective function J^k+1Then entering a convergence judgment module;

6) judging convergence conditions | J^k-J^k+1Whether zeta is less than or equal to J^kAnd J^k+1Respectively representing the objective function values obtained by the k-th and k + 1-th iterative computations, and if not, saving the objective value J^k+1Taking k as k +1, and then turning to the step 4) to perform a new round of iterative optimization; if so, terminating the iterative computation, z^k+1Is the optimal decision variable, J^k+1Is the optimal target value, save z^*、J^*And the iteration times (k +1) to a result output module.

Further, in the step 1), the data of the industrial process object collected by the on-site intelligent instrument is transmitted to a real-time database of the DCS system, the latest data obtained from the database of the DCS system in each sampling period is output to the upper computer, and initialization processing is performed by an initialization module of the upper computer.

Still further, in the step 6), the obtained optimal decision variable z^＊Converting the result into an optimal control curve u^*(t) and displaying u on the human-machine interface of the upper computer^*(t) and an optimum target value J^*(ii) a At the same time, the optimum control curve u^*And (t) transmitting the information to the DCS through the communication interface, and displaying the obtained optimization result information in the DCS.

The invention has the following beneficial effects: the method can find the solution of the optimal control problem of the nonlinear system in the industrial process, has high solving efficiency and good convergence stability, and therefore has wide application prospect in various fields of dynamic simulation and optimal control of the industrial process.

Drawings

FIG. 1 is a hardware block diagram of an industrial process optimization control system provided by the present invention;

fig. 2 is a schematic structure diagram of the upper computer implementing the optimal control method of the present invention.

Detailed Description

The present invention will be described in detail below with reference to the accompanying drawings.

Example 1

Referring to fig. 1 and 2, the adaptive industrial process optimal control system comprises a field intelligent instrument 2 connected with an industrial process object 1, a DCS system and an upper computer 6, wherein the DCS system is composed of a bus interface 3, an operation station 4 and a database 5; on-spot intelligent instrument 2, DCS system, host computer 6 pass through field bus and link to each other in proper order, the host computer include:

an initialization module 9, configured to set initial parameters, optimize discretization and initial assignment of the variable z (t), specifically includes the following steps:

(3.1) time domain [ t₀，t_f]The average division into n small segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]Wherein t is_n＝t_f(ii) a The length of each time segment is h ═ t (t)_f-t₀)/n；

(3.2) discretizing the optimization variable z (t) on the time segment (3.1), replacing z (t) with a variable z (namely a decision variable) consisting of n segment constants, and selecting an arbitrary constant as an initial value z of the decision variable⁰；

(3.3) setting a convergence precision value zeta for judging whether the iterative optimization is terminated or not (when the iterative error of the optimization target value is less than zeta, stopping iteration); taking an initial value of the iteration times k as 0;

(3.4) setting an initial step size alpha 0 of iterative search;

the constraint conversion module 8: and (3) processing the control variable boundary constraint in the optimization process through the intermediate variable, and adopting the following conversion equation:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

will have boundary constraint u_min≤u(t)≤u_maxIs replaced by a trigonometric function expression of an intermediate variable z (t) which is not bound by a boundary, where the indices min, max represent the minimum and maximum values, respectively, u (t)_min、u_maxRespectively corresponding to the lower bound and the upper bound of the control variable, and solving the z (t) as an optimization variable.

The adaptive solving module 10 is used for solving an ordinary differential equation set of an optimal control problem of an industrial process, providing state variable and covariate variable information for gradient calculation of the iterative optimization module 11, and providing objective function information for convergence condition judgment of the convergence judgment module 12, and the adaptive solving module is completed by adopting the following steps:

(4.1) solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0 i＝1，2，...，m (2)

wherein f represents a differential function variable, x (t) is a variable consisting of m state variables, x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀By the initial value x of the state variable_i0Determining the value x of the state variable at each discrete time by forward integration_i(t)，i＝1，2，...，m；

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><mi>d</mi><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>t</mi><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math> i＝1，2，...，m

(3)

wherein,

ψ is a given objective function

Non-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) Is a covariant lambda_iAt terminal time t_fBy a value of the covariate variable terminal λ_i(t_f) Determining the value lambda of the covariate at each discrete time by inverse integration_i(t)，i＝1，2，...，m；

(4.3) calculating an objective function value from the obtained state variables and decision variables:

an iterative optimization module 11 for searching a decision variable z for optimizing the objective function J^＊The method is completed by adopting the following steps, the superscripts k all represent the iteration times, and the initial assignment is zero:

(5.1) calling the adaptive solving module 10, and saving the obtained state variables, covariates and objective function values (namely the current objective value J)^k)

(5.2) calculating the current gradient g^k(superscript T denotes the transpose of the variable or matrix), i.e. the search direction of the iterative optimization:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msub><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if k is 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, determining the step factor l by iterating the information of the current point and the previous point^k：

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

Wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mo>=</mo><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Passes to an adaptive solution module to calculate a new objective function value J^k+1Then, the method enters a convergence judgment module 12;

the convergence judging module 12: for judging whether the target result obtained by the iterative optimization module 11 satisfies the convergence condition:

|J^k-J^k+1|≤ζ (11)

wherein J^kAnd J^k+1Respectively representing the objective function values obtained by the k-th iterative computation and the k + 1-th iterative computation. If the above formula (11) is satisfied, indicating that the absolute value of the error between the target value obtained by the current iteration and the target value obtained by the previous iteration does not exceed the set convergence precision ζ, stopping the iterative optimization calculation, and determining that zk +1 is the optimal decision variable z^*(＝z^k+1)，J^k+1Is the optimum target value J^*(＝J^k+1) Will z^*、J^*And the corresponding iteration times (k +1) are saved to the result output module 13; if the above equation (11) is not satisfied, the target value J is stored^k+1And taking k as k +1, and then returning to the iterative optimization module 11 to perform a new round of iterative solution.

The upper computer also comprises an information acquisition module 7 which is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument; and a result output module 13 for outputting the optimal decision trajectory z obtained by the iterative optimization module^*(t) (by variable z)^＊Time-phased representation) is converted into an optimal control trajectory u by the formula (1)^*(t) then adding u^*And (t) transmitting to the DCS, and displaying the obtained optimization result information in the DCS.

The system hardware structure diagram of this embodiment is shown in fig. 1, and the core of the optimal control system includes 5 large function modules, such as a constraint conversion module 8, an initialization module 9, an adaptive solving module 10, an iterative optimization module 11, and a convergence judgment module 12, in an upper computer 6 with a human-computer interface, and further includes: the field intelligent instrument 2, the DCS system and the field bus. The DCS system consists of a bus interface 3, an operation station 4 and a database 5; the industrial process object 1, the field intelligent instrument 2, the DCS system and the upper computer 6 are sequentially connected through a field bus to achieve uploading and issuing of information flow, and the upper computer and the bottom layer system timely exchange information to achieve online optimization of the system.

Example 2

Referring to fig. 1 and 2, an adaptive optimal control method for an industrial process, the optimal control method being implemented according to the following steps:

1) specifying state variables and control variables in a DCS system, and setting upper and lower boundaries u of the control variables according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd the sampling period of the DCS, and the historical data of corresponding variables in the DCS database 5, the upper and lower boundary values u of the control variables_max、u_minAnd transmitted to the upper computer 6.

2) In a constraint conversion module 8 of the upper computer, a control variable u (t) restricted by a boundary is subjected to element [ u ] by trigonometric function substitution_min，u_max]Conversion to another unconstrained variable z (t), namely:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

and then, performing optimization solution by taking z (t) as an optimization variable, and substituting the finally obtained z (t) into the formula (1) to obtain the corresponding u (t).

3) In an initialization module 9 of the upper computer, initial parameters of each module of the upper computer are set, and data input by a DCS (distributed control system) is initialized, and the initialization is completed according to the following steps:

(3.1) setting the time domain [ t ] of the optimal control₀，t_f]And a time segmentation number n, which equally divides the time domain into n segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]Each time segment has a length h ═ t (t)_f-t₀)/n；

(3.2) discretizing the optimization variable z (t) over (3.1) the time segmentZ (t) is expressed by using a variable z (i.e., a decision variable) composed of n piecewise constants, and an initial value z of the decision variable is selected⁰It may be taken as a simple constant;

(3.3) the convergence judging module 12 of the upper computer sets a convergence precision zeta value which is generally 10 according to the actual solving precision requirement^-6The requirements can be met. Setting the initial count of the optimized iteration times k to be 0;

(3.4) setting the initial step size alpha 0 of the iterative search to be more than 0;

4) the optimization variable z of the current iteration step is equal to z^k(when the number of iterations k is 0, z is z⁰) Substituting into the self-adaptive solving module to obtain the current state variable and the covariate and obtain the corresponding current target value J^k. The method comprises the following implementation steps:

(4.1) numerically solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0 i＝1，2，...，m (2)

wherein f represents a differential function variable, x (t) is an m-dimensional state variable, and x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀A value of (d);

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><mi>d</mi><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mi>t</mi><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math>

i＝1，2，...，m (3)

wherein,

ψ is a given objective function

Non-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) For the ith covariant lambda_iAt terminal time t_fA value of (d);

(4.3) calculating an objective function value from the obtained state variables and decision variables:

5) the iterative optimization is calculated by the state variable and the covariate information obtained by the adaptive solving module 10For finding the decision variable z that optimizes the objective function J^＊The method is completed by adopting the following steps, the superscripts k all represent the iteration times, and the initial assignment is zero:

(5.1) calling the calculation result in the step 4), and saving the obtained state variable, the obtained co-state variable and the obtained objective function value, wherein the objective function value is the current target value J^k；

(5.2) calculating the current gradient g^kI.e. the search direction of the iterative optimization (where x (T) and λ (T) are the current state variable and the covariate, respectively, obtained by the solution, and the superscript T represents the transpose of the variable or matrix:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msub><mrow><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if kWhen 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, determining the step factor l by iterating the information of the current point and the previous point^k：

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

Wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mo>=</mo><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Is transmitted to the adaptive solving module 10 to calculate a new objective function value J by the step (5.4)^k+1Then, the method enters a convergence judgment module 12;

6) the convergence judgment module 12 judges the convergence condition | J^k-J^k+1Whether or not | is less than or equal to (wherein J^kAnd J^k+1Respectively representing objective function values obtained by the k-th and k + 1-th iterative computations), if not, saving the objective value J^k+1Taking k as k +1, and then turning to the step 4) to perform a new round of iterative optimization; if so, terminating the iterative computation, z^k+1Is the optimal decision variable (denoted as z)^*＝z^k+1)，J^k+1Is the optimal target value (denoted as J)^*＝J^k+1) Preservation of z^*、J^*And the number of iterations (k +1) to the result output module 13.

System commissioning

A. Setting the time interval of each data detection and acquisition by using a timer;

B. the field intelligent instrument 2 detects the data of the industrial process object 1 and transmits the data to a real-time database 5 of the DCS system to obtain the latest variable data;

C. in a constraint conversion module 8 of the upper computer 6, processing the control variable boundary constraint, and taking the processing result as the input of an initialization module 9;

D. in an initialization module 9 of the upper computer 6, initializing relevant parameters and variables of each module according to actual production requirements and operation limiting conditions, and taking a processing result as input of an iterative optimization module 11;

E. the adaptive solving module 10 of the upper computer 6 solves the problem according to the initial decision variables or the iterative decision variables input by the iterative optimization module 11, and the obtained state variables, the obtained covariates and the obtained target values are transmitted back to the iterative optimization module 11;

F. the iterative optimization module 11 of the upper computer 6 performs gradient calculation according to the variable substitution relationship of the constraint conversion module 8 and the variable information obtained by the adaptive solving module 10, and performs iterative optimization according to the judgment result of the convergence judgment module 12, and the optimized result is transmitted to the result output module 13;

G. the convergence judging module 12 of the upper computer 6 judges whether to terminate the iterative optimization according to the convergence condition, and the obtained result is transmitted to the iterative optimization module 11 and the result output module 13.

The result information of the optimal control of the industrial process is displayed on a human-computer interface of the upper computer 6, the upper computer 6 transmits the obtained optimal control curve to the DCS, the obtained optimal result information is displayed on an operation station 4 of the DCS, the obtained optimal result information is transmitted to a field work station for display through the DCS and a field bus, and the field work station executes the optimal operation.

The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the appended claims.

Claims (6)

1. The utility model provides an industrial process optimal control system of self-adaptation, includes on-spot intelligent instrument, DCS system and the host computer of being connected with industrial process object, intelligent detection instrument, DCS system and host computer link to each other its characterized in that in proper order: the host computer include:

the initialization module is used for setting initial parameters, optimizing discretization and initial assignment of variables z (t), and comprises the following specific steps:

(3.1) time domain [ t₀，t_f]The average division into n small segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]Wherein t is_n＝t_f(ii) a The length of each time segment is h ═ t (t)_f-t₀) N, where t₀Denotes the starting time, t_fIndicating a termination time;

(3.2) discretizing the optimized variable z (t) on the time segment (3.1), replacing z (t) with a variable z consisting of n segment constants, and selecting an arbitrary constant as an initial value z of a decision variable⁰；

(3.3) setting a convergence precision value zeta for judging whether the iterative optimization is terminated, and stopping the iteration when the iterative error of the optimization target value is smaller than zeta; taking an initial value of the iteration times k as 0;

(3.4) setting an initial step size alpha 0 of iterative search;

the constraint conversion module is used for processing the control variable boundary constraint in the optimization process through the intermediate variable and adopting the following conversion equation:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

will have boundary constraint u_min≤u(t)≤u_maxIs replaced by a trigonometric function expression of an intermediate variable z (t) which is not bound by a boundary, where the indices min, max represent the minimum and maximum values, respectively, u (t)_min、u_maxRespectively corresponding to the lower bound and the upper bound of the control variable, and solving by taking z (t) as an optimization variable;

the self-adaptive solving module is used for solving a normal differential equation set of an optimal control problem of the industrial process, providing state variable and covariate variable information for gradient calculation of the iterative optimization module, and providing target function information for convergence condition judgment of the convergence judgment module, and is completed by adopting the following steps:

(4.1) solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0(i＝1，2，，m) (2)

wherein f represents a differential function variable, x (t) is a variable consisting of m state variables, x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀A value of (d);

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><msub><mi>d&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math>

i＝1，2，...，m

(3)

wherein,

ψ is a given objective function

Non-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) Is a covariant lambda_iAt terminal time t_fA value of (d);

(4.3) calculating an objective function value from the obtained state variables and decision variables:

an iterative optimization module for searching a decision variable z for optimizing an objective function J^＊The method is completed by adopting the following steps, the superscripts k all represent the iteration times, and the initial assignment is zero:

(5.1) calling an adaptive solving module, and saving the obtained state variable, the obtained co-state variable and the obtained objective function value, wherein the objective function value is the current target value J^k；

(5.2) calculating the current gradient g^kThe superscript T represents the transpose of the variable or matrix, i.e. the search direction of the iterative optimization:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><msub><mrow><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if k is 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, the step factor l is determined by iterating the information of the current point and the previous point^k：

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

Wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mo>=</mo><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Passes to an adaptive solution module to calculate a new objective function

Number J^k+1Then entering a convergence judgment module;

a convergence judgment module: the method is used for judging whether the target result obtained by the iteration optimizing module meets the convergence condition:

|J^k-J^k+1|≤ζ (11)

wherein, J^kAnd J^k+1Respectively representing objective function values obtained by the k-th iterative computation and the (k +1) -th iterative computation, stopping the iterative optimization computation if the above expression (11) is satisfied, and the absolute value of the error between the target value obtained by the current iteration and the target value obtained by the previous iteration is not more than the set convergence precision zeta, and z is^k+1Is the optimal decision variable z^*(＝z^k+1)，J^k+1Is the optimum target value J^*(＝J^k+1) Will z^*、J^*And the corresponding iteration times (k +1) are saved in a result output module; if the above equation (11) is not satisfied, the target value J is stored^k+1And taking k as k +1, and then returning to the iterative optimization module to perform a new round of iterative solution.

2. An adaptive industrial process optimal control system according to claim 1, characterized in that: the upper computer also comprises an information acquisition module which is used for setting sampling time and acquiring dynamic information of the industrial process object uploaded by the on-site intelligent instrument.

3. According to claim 1 or2 the adaptive industrial process optimal control system is characterized in that: the upper computer also comprises a result output module which is used for outputting the optimal decision trajectory z obtained by the iteration optimizing module^*(t) conversion into an optimal control trajectory u by equation (1)^*(t), optimal decision trajectory z^*(t) is represented by the variable z^＊Expressed in time intervals, then u is^*And (t) transmitting to the DCS, and displaying the obtained optimization result information in the DCS.

4. An optimal control method implemented by an adaptive optimal control system of an industrial process according to claim 1, wherein: the optimal control method comprises the following steps:

1) specifying state variables and control variables in a DCS system, and setting upper and lower boundaries u of the control variables according to conditions of an actual production environment and conditions of operation restrictions_max、u_minAnd the sampling period of the DCS, and the historical data of corresponding variables in the DCS database, the upper and lower boundary values u of the control variables_max、u_minTransmitting to an upper computer;

2) and (3) processing the control variable boundary constraint in the optimization process through the intermediate variable, and adopting the following conversion equation:

u(t)＝0.5(u_max-u_min)×{cos[z(t)]+1}+u_min (1)

will have boundary constraint u_min≤u(t)≤u_maxIs replaced by a trigonometric function expression of an intermediate variable z (t) which is not bound by a boundary, where the indices min, max represent the minimum and maximum values, respectively, u (t)_min、u_maxRespectively corresponding to the lower bound and the upper bound of the control variable, and solving by taking z (t) as an optimization variable;

3) setting initial parameters of the module, initializing data input by a DCS, and completing the steps as follows:

(3.1) time domain [ t₀，t_f]The average division into n small segments: [ t ] of₀，t₁]，[t₁，t₂]，…，[t_n-1，t_n]Wherein t is_n＝t_f(ii) a The length of each time segment is h ═ t (t)_f-t₀) N, where t₀Denotes the starting time, t_fIndicating a termination time;

(3.2) discretizing the optimized variable z (t) on the time segment (3.1), replacing z (t) with a variable z consisting of n segment constants, and selecting an arbitrary constant as an initial value z of a decision variable⁰；

(3.3) setting a convergence precision value zeta for judging whether the iterative optimization is terminated, and stopping the iteration when the iterative error of the optimization target value is smaller than zeta; taking an initial value of the iteration times k as 0;

(3.4) setting the initial step size alpha 0 of the iterative search to be more than 0;

4) the optimization variable z of the current iteration step is equal to z^kSubstituting into the self-adaptive solving module, and when the iteration number k is 0, z is equal to z⁰Calculating the current state variable and the covariate and obtaining the corresponding current target value J^kThe method comprises the following implementation steps:

(4.1) solving a system of state equations:

$\frac{\mathrm{dx}\left(t\right)}{\mathrm{dt}}=f[x\left(t\right),z\left(t\right),t],$ x_i(t₀)＝x_i0(i＝1，2，...，m) (2)

wherein f represents a differential function variable, x (t) is a variable consisting of m state variables, x_i(t) denotes the i-th state variable, x_i0Is a state variable x_iAt an initial time t₀A value of (d);

(4.2) solving a collaborative system of equations:

<math><mrow><mfrac><mrow><msub><mi>d&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi>dt</mi></mfrac><mo>=</mo><mo>-</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>-</mo><msub><mi>&lambda;</mi><mi>i</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><msub><mrow><mo>&PartialD;</mo><mi>x</mi></mrow><mi>i</mi></msub></mfrac><mo>,</mo></mrow></math> i＝1，2，...，m

(3)

wherein,

ψ is a given objective function

Non-integral term and constant integral term of (a)_i(t) is the ith covariant, λ (t) is the variable composed of m covariants, λ_i(t_f) Is a covariant lambda_iAt terminal time t_fA value of (d);

(4.3) calculating an objective function value from the obtained state variables and decision variables:

5) calculating the search direction and step length of iterative optimization by the state variable and the covariate information obtained by the self-adaptive solving module, solving the decision variable z which enables the objective function J to be closer to the optimal value, and implementing the iterative optimization, wherein the superscript k represents the iteration times, and the initial assignment is zero:

(5.1) calling the calculation result in the step 4), and saving the obtained state variable, the obtained co-state variable and the obtained objective function value, wherein the objective function value is the current target value J^k；

(5.2) calculating the current gradient g^kThe superscript T represents the transpose of the variable or matrix, i.e. the search direction of the iterative optimization:

<math><mrow><msup><mi>g</mi><mi>k</mi></msup><mo>=</mo><msub><mrow><mo>{</mo><mfrac><mrow><mo>&PartialD;</mo><mi>&psi;</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi><mo>]</mo></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>+</mo><mi>&lambda;</mi><msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><mfrac><mrow><mo>&PartialD;</mo><mi>f</mi><mo>[</mo><mi>x</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mi>t</mi></mrow><mrow><mo>&PartialD;</mo><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></mfrac><mo>}</mo><mo>|</mo></mrow><mrow><mi>z</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msup><mi>z</mi><mi>k</mi></msup><mo>,</mo><mi>t</mi><mo>=</mo><msub><mi>t</mi><mi>j</mi></msub></mrow></msub><mo>,</mo></mrow></math> j＝0，1，2，...，n (5)

(5.3) saving the current iteration point z^kAnd gradient information g^k；

(5.4) if k is 0, the search step α is determined^kTake as an initial value, i.e. alpha^kTurning to step (5.6) when the value is alpha 0;

otherwise, the step factor lk is determined by iterating the information of the current point and the previous point:

<math><mrow><msup><mi>l</mi><mi>k</mi></msup><mo>=</mo><mfrac><mrow><msup><mrow><mo>(</mo><msup><mi>s</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow><mi>T</mi></msup><mo>&CenterDot;</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup></mrow><msup><mrow><mo>|</mo><mo>|</mo><msup><mi>y</mi><mrow><mi>k</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>|</mo><mo>|</mo></mrow><mn>2</mn></msup></mfrac><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>6</mn><mo>)</mo></mrow></mrow></math>

wherein s is^k-1And representing the error between the current iteration point and the previous iteration point, and calculating as follows:

s^k-1＝z^k-z^k-1 (7)

y^k-1and representing the gradient error of the current iteration point and the previous iteration point, and calculating as follows:

y^k-1＝g^k-g^k-1 (8)

(5.5) taking the optimal step size <math><mrow><msup><mi>&alpha;</mi><mi>k</mi></msup><mi>min</mi><mrow><mo>(</mo><mfrac><mi>&pi;</mi><mrow><mi>D</mi><mo>&CenterDot;</mo><mi>max</mi><mrow><mo>(</mo><msup><mi>g</mi><mi>k</mi></msup><mo>)</mo></mrow></mrow></mfrac><mo>,</mo><msup><mi>l</mi><mi>k</mi></msup><mo>)</mo></mrow><mo>-</mo><mo>-</mo><mo>-</mo><mrow><mo>(</mo><mn>9</mn><mo>)</mo></mrow></mrow></math>

Wherein D is a coefficient integer value;

(5.6) calculating the next iteration point:

z^k+1＝z^k-α^k·g^k (10)

(5.7) new iteration point z^k+1Passes to step (5.4) to calculate a new value of the objective function J^k+1Then entering a convergence judgment module;

6) judging convergence conditions | J^k-J^k+1Whether zeta is less than or equal to J^kAnd J^k+1Respectively representing the objective function values obtained by the k-th and k + 1-th iterative computations, and if not, saving the objective value J^k+1Taking k as k +1, and then turning to the step 4) to perform a new round of iterative optimization; if so, terminating the iterative computation, z^k+1Is the optimal decision variable, J^k+1Is the optimal target value, save z^*、J^*And the iteration times (k +1) to a result output module.

5. The optimum control method according to claim 4, wherein: in the step 1), the data of the industrial process object acquired by the on-site intelligent instrument is transmitted to a real-time database of the DCS, the latest data obtained from the database of the DCS in each sampling period is output to the upper computer, and initialization processing is carried out by an initialization module of the upper computer.

6. The optimum control method according to claim 4 or 5, wherein: the optimal decision variable z obtained in the step 6)^＊Converting the result into an optimal control curve u^*(t) and displaying u on the human-machine interface of the upper computer^*(t) and an optimum target value J^*(ii) a At the same time, the optimum control curve u^*And (t) transmitting the information to the DCS through the communication interface, and displaying the obtained optimization result information in the DCS.

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